Problem: Graph this system of equations and solve. $-4x-10y = -30$ $-6x+10y = -20$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Solution: Convert the first equation, $-4x-10y = -30$ , to slope-intercept form. $y = -\dfrac{2}{5} x + 3$ The y-intercept for the first equation is $3$ , so the first line must pass through the point $(0, 3)$ The slope for the first equation is $-\dfrac{2}{5}$ . Remember that the slope tells you rise over run. So in this case for every $2$ positions you move down (because it's negative) You must also move $5$ positions to the right. $5$ positions to the right. $2$ positions down from $(0, 3)$ is $(5, 1)$ Graph the blue line so it passes through $(0, 3)$ and $(5, 1)$ Convert the second equation, $-6x+10y = -20$ , to slope-intercept form. $y = \dfrac{3}{5} x - 2$ The y-intercept for the second equation is $-2$ , so the second line must pass through the point $(0, -2)$ The slope for the second equation is $\dfrac{3}{5}$ . Remember that the slope tells you rise over run. So in this case for every $3$ positions you move up You must also move $5$ positions to the right. $5$ positions to the right. $3$ positions up from $(0, -2)$ is $(5, 1)$ Graph the green line so it passes through $(0, -2)$ and $(5, 1)$ The solution is the point where the two lines intersect. The lines intersect at $(5, 1)$.